One sunny summer morning, a smartly dressed young man who appeared to be a gentleman arrived to visit a renowned

, let"s move on to the next one.

The dentist, concerned about the man"s behavior, decided to test his honesty. He had a small dish with five similarly shaped silver coins - four real ones and one counterfeit. The genuine coins all weighed the same, while the fake coin weighed slightly less. The dentist took the five coins and handed them to the man, asking him to determine which one was the counterfeit using only a balance scale.

The dentist explained that the man could use the scale only three times. If he succeeded in identifying the fake coin within those three weighings, he would be allowed to keep it as a reward. However, if he failed, he would be required to return any coins he had taken from the waiting room.

The man understood the rules and began thinking about the best strategy to identify the counterfeit coin. He knew he had to be efficient, as he only had three weighings available.

Now, let"s break down the problem step by step.

Step 1: Divide the coins into three groups, two groups with two coins each, and one group with just one coin. Label them as Group A, Group B, and Group C.

Step 2: For the first weighing, compare Group A and Group B by placing them on separate sides of the scale. If they balance each other out, it means the counterfeit coin is in Group C. If one side is lighter, it means the fake coin is in the lighter group.

Step 3: Now that we know which group contains the counterfeit coin, let"s call it Group X. Take one of the coins from Group X and place it on one side of the scale. Take another coin from Group X and place it on the other side of the scale.

- If both sides balance each other out, it means the remaining coin in Group X is the fake one. If one side is lighter, it means the lighter coin is the counterfeit.

Step 4: We have determined which coin is the counterfeit, and this is our final weighing. Weigh the counterfeit coin against any genuine coin, and the lighter one will be the fake.

To summarize, the man needs to:
- Divide the coins into three groups: Group A, Group B, and Group C.
- Weigh Group A against Group B to determine which group contains the fake coin.
- Weigh two coins from the identified group against each other to narrow down the search.
- Finally, compare the identified counterfeit coin with a genuine coin to find the lighter one and identify it as the fake coin.

Using this strategy, the gentleman should be able to identify the counterfeit coin within the three weighings.